Asymptotic properties of some classes of generalized functions

This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Cesáro convergence (with respect to a self-similar weight) of the Fourier–Stieltjes series of nonnegative measures.
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